NCERT Solutions
Class 11 - Mathematics

Chapter 6: PERMUTATIONS AND COMBINATIONS

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed and also when repetition is not allowed?

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

How many 4-letter codes can be formed using the first 10 letters of the English alphabet if no letter can be repeated?

How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Evaluate:

(i) \(8!\)

(ii) \(4! - 3!\)

Is \(3! + 4! = 7!\)?

Compute \(\dfrac{8!}{6! \times 2!}\)

If \(\dfrac{1}{6!} + \dfrac{1}{7!} = \dfrac{x}{8!}\), find \(x\)

Evaluate \(\dfrac{n!}{(n-r)!}\) for:

(i) \(n = 6, r = 2\)

(ii) \(n = 9, r = 5\)

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

How many 4-digit numbers are there with no digit repeated?

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

From a committee of 8 persons, in how many ways can we choose a chairman and a vice-chairman assuming one person cannot hold more than one position?

Find n if \( {}^{n-1}P_3 : {}^nP_4 = 1 : 9 \).

Find r if (i) \( {}^{5}P_r = 2 \cdot {}^{6}P_{r-1} \) (ii) \( {}^{5}P_r = {}^{6}P_{r-1} \).

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

How many words, with or without meaning, can be made from the letters of the word MONDAY, assuming that no letter is repeated?
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?

In how many ways can the letters of the word PERMUTATIONS be arranged if the:
(i) words start with P and end with S,
(ii) vowels are all together,
(iii) there are always 4 letters between P and S?

If \( ^nC_8 = ^nC_2 \), find \( ^nC_2 \).

Determine \( n \) if

(i) \( ^{2n}C_3 : ^nC_3 = 12 : 1 \)

(ii) \( ^{2n}C_3 : ^nC_3 = 11 : 1 \)

How many chords can be drawn through 21 points on a circle?

In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Determine the number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?